Practice some problems that involve thinking about the conditions for obtaining extraneous solutions while solving radical equations.


Divya is solving the following equation for w.
3, w, minus, square root of, 20, minus, 5, w, end square root, equals, 2
Her first few steps are given below.
3w=205w+23w2=205w(3w2)2=(205w)29w212w+4=205w\begin{aligned} 3w&=\sqrt{20-5w}+2\\ \\ 3w-2&=\sqrt{20-5w}\\ \\ (3w-2)^2&=\left(\sqrt{20-5w}\right)^2\\ \\ 9w^2-12w+4&=20-5w \end{aligned}
Is it necessary for Divya to check her answers for extraneous solutions?
Please choose from one of the following options.